未读消息消息

购物车

我的订单

个人中心

店铺

我的订单收藏

拍卖

拍卖交易我的竞拍收藏

我的好友资金账户

卖家中心

客服 |

帮助中心 9:00-20:30 在线留言

客服电话

010-89648155

服务时间

客服咨询 8:00-21:00

纠纷处理 9:00-21:00

图书审核 9:00-18:00

监督与建议

请选择

手机孔网

时间序列分析：预测与控制

作者: [美] GeorgeE.P.Box 著 , [英] GwilymM.Jenkins 著 , [美] GregoryC.Reinsel 著

出版社: 人民邮电出版社

出版时间: 2005-09

版次: 1

ISBN: 9787115137722

定价: 65.00

装帧: 平装

开本: 16开

纸张: 胶版纸

页数: 598页

字数: 840千字

正文语种: 英语

丛书: 图灵原版数学·统计学系列

分类: 教材教辅考试>教材>大学教材>经济

45人买过

　　本书自1970年初版以来，不断修订再版，以其经典性和权威性成为有关时间序列分析领域书籍的典范。书中涉及时间序列随机(统计)模型的建立及许多重要的应用领域的使用，包括预测，模型的描述、估计、识别和诊断，动态关系的传递函数的识别、拟合及检验，干预事件影响的建模和过程控制等专题。本书叙述简明，强调实际技术，配有大量实例。
　　本书可作为统计和相关专业高年级本科生或研究生教材，也可以作为统计专业技术人员的参考书。　　GeorgeE.P.Box国际级统计学家。曾于1960年创立威斯康星大学统计系并任该系主任，现为该校名誉教授。BOX发表过200多篇论文，出版过很多重要著作，其中本书和STATISTICEFOR
　　EXPERIMENTERS为其代表作。
　　GwilymM.Jenkins已故国际级统计学家。曾于1966年创立了英国兰开斯特大学系统工程系。JENKINS与BOX合作的成果对时间序列分析方法的研究和应用产生了巨大的推动作用。
　　GregoryC.Reinsel已故国际级统计学家。1995-1997年任威斯康星大学统计系系主任。因在统计领域的突出贡献而被推举为美国统计协会会士。 1　INTRODUCTION　1
1.1　FourImportantPracticalProblems　2
1.1.1　ForecastingTimeSeries　2
1.1.2　EstimationofTransferFunctions　3
1.1.3　AnalysisofEffectsofUnusualInterventionEventsToaSystem　4
1.1.4　DiscreteControlSystems　5
1.2　StochasticandDeterministicDynamicMathematicalModels　7
1.2.1　StationaryandNonstationaryStochasticModelsforForecastingandControl　7
1.2.2　TransferFunctionModels　12
1.2.3　ModelsforDiscreteControlSystems　14
1.3　BasicIdeasinModelBuilding　16
1.3.1　Parsimony　16
1.3.2　IterativeStagesintheSelectionofaModel　16

PartI　StochasticModelsandTheirForecasting　19

2　AUTOCORRELATIONFUNCTIONANDSPECTRUMOFSTATIONARYPROCESSES　21
2.1　AutocorrelationPropertiesofStationaryModels　21
2.1.1　TimeSeriesandStochasticProcesses　21
2.1.2　StationaryStochasticProcesses　23
2.1.3　PositiveDefinitenessandtheAutocovarianceMatrix　26
2.1.4　AutocovarianceandAutocorrelationFunctions　29
2.1.5　EstimationofAutocovarianceandAutocorrelationFunctions　30
2.1.6　StandardErrorofAutocorrelationEstimates　32
2.2　SpectralPropertiesofStationaryModels　35
2.2.1　PeriodogramofaTimeSeries　35
2.2.2　AnalysisofVariance　36
2.2.3　SpectrumandSpectralDensityFunction　37
2.2.4　SimpleExamplesofAutocorrelationandSpectralDensityFunctions　41
2.2.5　AdvantagesandDisadvantagesoftheAutocorrelationandSpectralDensityFunctions　43
A2.1　LinkBetweentheSampleSpectrumandAutocovarianceFunctionEstimate　44

3　LINEARSTATIONARYMODELS　46
3.1　GeneralLinearProcess　46
3.1.1　TwoEquivalentFormsfortheLinearProcess　46
3.1.2　AutocovarianceGeneratingFunctionofaLinearProcess　49
3.1.3　StationarityandInvertibilityConditionsforaLinearProcess　50
3.1.4　AutoregressiveandMovingAverageProcesses　52
3.2　AutoregressiveProcesses　54
3.2.1　StationarityConditionsforAutoregressiveProcesses　54
3.2.2　AutocorrelationFunctionandSpectrumofAutoregressiueProcesses　55
3.2.3　First-OrderAutoregressive(Markov)Process　58
3.2.4　Second-OrderAutoregressiveProcess　60
3.2.5　PartialAutocorrelationFunction　64
3.2.6　EstimationofthePartialAutocorrelationFunction　67
3.2.7　StandardErrorsofPartialAutocorrelationEstimates　68
3.3　MovingAverageProcesses　69
3.3.1　InvertibilityConditionsforMovingAverageProcesses　69
3.3.2　AutocorrelationFunctionandSpectrumofMovingAverageProcesses　70
3.3.3　First-OrderMovingAverageProcess　72
3.3.4　Second-OrderMovingAverageProcess　73
3.3.5　DualityBetweenAutoregressiveandMovingAverageProcesses　75
3.4　MixedAutoregressive-MovingAverageProcesses　77
3.4.1　StationarityandInvertibilityProperties　77
3.4.2　AutocorrelationFunctionandSpectrumofMixedProcesses　78
3.4.3　First-OrderAutoregressive-First-OrderMovingAverageProcess　80
3.4.4　Summary　83
A3.1　AutocovariancesAutocovarianceGeneratingFunctionandStationarityConditionsforaGeneralLinearProcess　85
A3.2　RecursiveMethodforCalculatingEstimatesofAutoregressiveParameters　87

4　LINEARNONSTATIONARYMODELS　89
4.1　AutoregressiveIntegratedMovingAverageProcesses　89
4.1.1　NonstationaryFirst-OrderAutoregressiveProcess　89
4.1.2　GeneralModelforaNonstationaryProcessExhibitingHomogeneity　92
4.1.3　GeneralFormoftheAutoregressiveIntegratedMovingAverageProcess　96
4.2　ThreeExplicitFormsfortheAutoregressiveIntegratedMovingAverageModel　99
4.2.1　DifferenceEquationFormoftheModel　99
4.2.2　RandomShockFormoftheModel　I00
4.2.3　InvertedFormoftheModel　106
4.3　IntegratedMovingAverageProcesses　109
4.3.1　IntegratedMovingAverageProcessofOrder(0,1,1)　110
4.3.2　IntegratedMovingAverageProcessofOrder(0,2,2)　114
4.3.3　GeneralIntegratedMovingAverageProcessofOrder(0,d,q)　118
A4.1　LinearDifferenceEquations　120
A4.2　IMA(0,1,1)ProcessWithDeterministicDrift　125
A4.3　ARIMAProcessesWithAddedNoise　126
A4.3.1　SumofTwoIndependentMovingAverageProcesses　126
A4.3.2　EffectofAddedNoiseontheGeneralModel　127
A4.3.3　ExampleforanIMA(O,1,1)ProcesswithAddedWhiteNoise　128
A4.3.4　RelationBetweentheIMA(O,1,1)ProcessandaRandomWalk　129
A4.3.5　AutocovarianceFunctionoftheGeneralModelwithAddedCorrelatedNoise　129

5　FORECASTING　131
5.1　MinimumMeanSquareErrorForecastsandTheirProperties　131
5.1.1　DerivationoftheMinimumMeanSquareErrorForecasts　133
5.1.2　ThreeBasicFormsfortheForecast　135
5.2　CalculatingandUpdatingForecasts　139
5.2.1　ConvenientFormatfortheForecasts　139
5.2.2　CalculationoftheψWeights　139
5.2.3　UseoftheψWeightsinUpdatingtheForecasts　141
5.2.4　CalculationoftheProbabilityLimitsoftheForecastsatAnyLeadTime　142
5.3　ForecastFunctionandForecastWeights　145
5.3.1　EventualForecastFunctionDeterminedbytheAutoregressiveOperator　146
5.3.2　RoleoftheMooingAverageOperatorinFixingtheInitialValues　147
5.3.3　LeadlForecastWeights　148
5.4　ExamplesofForecastFunctionsandTheirUpdating　151
5.4.1　ForecastinganIMA(O,1,1)Process　151
5.4.2　ForecastinganIMA(O,2,2)Process　154
5.4.3　ForecastingaGeneralIMA(O,d,q)Process　156
5.4.4　ForecastingAutoregressiveProcesses　157
5.4.5　Forecastinga(1,O,1)Process　160
5.4.6　Forecastinga(1,1,1)Process　162
5.5　UseofStateSpaceModelFormulationforExactForecasting　163
5.5.1　StateSpaceModelRepresentationfortheARIMAProcess　163
5.5.2　KalmanFilteringRelationsforUseinPrediction　164
5.6　Summary　166
A5.1　CorrelationsBetweenForecastErrors　169
A5.1.1　AutocorrelationFunctionofForecastErrorsatDifferentOrigins　169
A5.1.2　CorrelationBetweenForecastErrorsattheSameOriginwithDifferentLeadTimes　170
A5.2　ForecastWeightsforAnyLeadTime　172
A5.3　ForecastinginTermsoftheGeneralIntegratedForm　174
A5.3.1　GeneralMethodofObtainingtheIntegratedForm　174
A5.3.2　UpdatingtheGeneralIntegratedForm　176
A5.3.3　ComparisonwiththeDiscountedLeastSquaresMethod　176

PartII　StochasticModelBuilding　181

6　MODELDENTIFICATION　183
6.l　ObjectivesofIdentification　183
6.1.1　StagesintheIdentificationProcedure　184
6.2　IdentificationTechniques　184
6.2.1　UseoftheAutocorrelationandPartialAutocorrelationFunctionsinIdentification　184
6.2.2　StandardErrorsforEstimatedAutocorrelationsandPartialAutocorrelations　188
6.2.3　IdentificationofSomeActualTimeSeries　188
6.2.4　SomeAdditionalModelIdentificationTools　197
6.3　InitialEstimatesfortheParameters　202
6.3.1　UniquenessofEstimatesObtainedfromtheAutocovarianceFunction　202
6.3.2　InitialEstimatesforMovingAverageProcesses　202
6.3.3　InitialEstimatesforAutoregressiveProcesses　204
6.3.4　InitialEstimatesforMixedAutoregressive-MovingAverageProcesses　206
6.3.5　ChoiceBetweenStationaryandNonstationaryModelsinDoubtfulCases　207
6.3.6　MoreFormalTestsforUnitRootsinARIMAModels　208
6.3.7　InitialEstimateofResidualVariance　211
6.3.8　ApproximateStandardErrorfor　212
6.4　ModelMultiplicity　214
6.4.1　MultiplicityofAutoregressive-MovingAverageModels　214
6.4.2　MultipleMomentSolutionsforMovingAverageParameters　216
6.4.3　UseoftheBackwardProcesstoDetermineStartingValues　218
A6.1　ExpectedBehavioroftheEstimatedAutocorrelationFunctionforaNonstationaryProcess　218
A6.2　GeneralMethodforObtainingInitialEstimatesoftheParametersofaMixedAutoregressive-MovingAverageProcess　220

7　MODELESTIMATION　224
7.l　StudyoftheLikelihoodandSumofSquaresFunctions　224
7.1.1　LikelihoodFunction　224
7.1.2　ConditionalLikelihoodforanARIMAProcess　226
7.1.3　ChoiceofStartingValuesforConditionalCalculation　227
7.1.4　UnconditionalLikelihood;SumofSquaresFunction;LeastSquaresEstimates　228
7.1.5　GeneralProcedureforCalculatingtheUnconditionalSumofSquares　233
7.1.6　GraphicalStudyoftheSumofSquaresFunction　238
7.1.7　Descriptionof“Well-Behaved”EstimationSituations;ConfidenceRegions　241
7.2　NonlinearEstimation　248
7.2.1　GeneralMethodofApproach　248
7.2.2　NumericalEstimatesoftheDerivatives　249
7.2.3　DirectEvaluationoftheDerivatives　251
7.2.4　GeneralLeastSquaresAlgorithmfortheConditionalModel　252
7.2.5　SummaryofModelsFittedtoSeriesAtoF　255
7.2.6　Large-SampleInformationMatricesandCovarianceEstimates　256
7.3　SomeEstimationResultsforSpecificModels　259
7.3.1　AutoregressiveProcesses　260
7.3.2　MovingAverageProcesses　262
7.3.3　MixedProcesses　262
7.3.4　SeparationofLinearandNonlinearComponentsinEstimation　263
7.3.5　ParameterRedundancy　264
7.4　EstimationUsingBayesTheorem　267
7.4.1　BayesTheorem　267
7.4.2　BayesianEstimationofParameters　269
7.4.3　AutoregressiveProcesses　270
7.4.4　MovingAverageProcesses　272
7.4.5　Mixedprocesses　274
7.5　LikelihoodFunctionBasedonTheStateSpaceModel　275
A7.1　ReviewofNormalDistributionTheory　279
A7.1.1　PartitioningofaPositive-DefiniteQuadraticForm　279
A7.1.2　TwoUsefulIntegrals　280
A7.1.3　NormalDistribution　281
A7.1.4　Studentst-Distribution　283
A7.2　ReviewofLinearLeastSquaresTheory　286
A7.2.1　NormalEquations　286
A7.2.2　EstimationofResidualVariance　287
A7.2.3　CovarianceMatrixofEstimates　288
A7.2.4　ConfidenceRegions　288
A7.2.5　CorrelatedErrors　288
A7.3　ExactLikelihoodFunctionforMovingAverageandMixedProcesses　289
A7.4　ExactLikelihoodFunctionforanAutoregressiveProcess　296
A7.5　ExamplesoftheEffectofParameterEstimationErrorsonProbabilityLimitsforForecasts　304
A7.6　SpecialNoteonEstimationofMovingAverageParameters　307

8　MODELDIAGNOSTICCHECKING　308
8.1　CheckingtheStochasticModel　308
8.1.1　GeneralPhilosophy　308
8.1.2　Overfitting　309
8.2　DiagnosticChecksAppliedtoResiduals　312
8.2.1　AutocorrelationCheck　312
8.2.2　PortmanteauLack-of-FitTest　314
8.2.3　ModelInadequacyArisingfromChangesinParameterValues　317
8.2.4　ScoreTestsforModelChecking　318
8.2.5　CumulativePeriodogramCheck　321
8.3　UseofResidualstoModifytheModel　324
8.3.1　NatureoftheCorrelationsintheResidualsWhenanIncorrectModelIsUsed　324
8.3.2　UseofResidualstoModifytheModel　325

9　SEASONALMODELS　327
9.1　ParsimoniousModelsforSeasonalTimeSeries　327
9.1.1　FittingversusForecasting　328
9.1.2　SeasonalModelsInvolvingAdaptiveSinesandCosines　329
9.1.3　GeneralMultiplicativeSeasonalModel　330
9.2　RepresentationoftheAirlineDatabyaMultiplicative(0,1,1)~(0,1,1)12SeasonalModel　333
9.2.1　Multiplicative(0,l,l)~(0,l,1)12Model　333
9.2.2　Forecasting　334
9.2.3　Identification　341
9.2.4　Estimation　344
9.2.5　DiagnosticChecking　349
9.3　SomeAspectsofMoreGeneralSeasonalModels　351
9.3.1　MultiplicativeandNonmultiplicativeModels　351
9.3.2　Identification　353
9.3.3　Estimation　355
9.3.4　EventualForecastFunctionsforVariousSeasonalModels　355
9.3.5　ChoiceofTransformation　358
9.4　StructuralComponentModelsandDeterministicSeasonalComponents　359
9.4.1　DeterministicSeasonalandTrendComponentsandCommonFactors　360
9.4.2　ModelswithRegressionTermsandTimeSeriesErrorTerms　361
A9.1　AutocovariancesforSomeSeasonalModels　366

PartIII　TransferFunctionModelBuilding　371

10　TRANSFERFUNCTIONMODELS　373
10.1　LinearTransferFunctionModels　373
10.1.1　DiscreteTransferFunction　374
10.1.2　ContinuousDynamicModelsRepresentedbyDifferentialEquations　376
10.2　DiscreteDynamicModelsRepresentedbyDifferenceEquations　381
10.2.1　GeneralFormoftheDifferenceEquation　381
10.2.2　NatureoftheTransferFunction　383
10.2.3　First-andSecond-OrderDiscreteTransferFunctionModels　384
10.2.4　RecursiveComputationofOutputforAnyInput　390
10.2.5　TransferFunctionModelswithAddedNoise　392
10.3　RelationBetweenDiscreteandContinuousModels　392
10.3.1　ResponsetoaPulsedInput　393
10.3.2　RelationshipsforFirst-andSecond-OrderCoincidentSystems　395
10.3.3　ApproximatingGeneralContinuousModelsbyDiscreteModels　398
A10.1　ContinuousModelsWithPulsedInputs　399
A10.2　NonlinearTransferFunctionsandLinearization　404

11　IDENTIFICATIONFITTINGANDCHECKINGOFTRANSFERFUNCTIONMODELS　407
ll.1　CrossCorrelationFunction　408
11.1.1　PropertiesoftheCrossCovarianceandCrossCorrelationFunctions　408
11.1.2　EstimationoftheCrossCovarianceandCrossCorrelationFunctions　411
11.1.3　ApproximateStandardErrorsofCrossCorrelationEstimates　413
11.2　IdentificationofTransferFunctionModels　415
11.2.1　IdentificationofTransferFunctionModelsbyPrewhiteningtheInput　417
11.2.2　ExampleoftheIdentificationofaTransferFunctionModel　419
11.2.3　IdentificationoftheNoiseModel　422
11.2.4　SomeGeneralConsiderationsinIdentifyingTransferFunctionModels　424
11.3　FittingandCheckingTransferFunctionModels　426
11.3.1　ConditionalSumofSquaresFunction　426
11.3.2　NonlinearEstimation　429
11.3.3　UseofResidualsforDiagnosticChecking　431
11.3.4　SpecificChecksAppliedtotheResiduals　432
11.4　SomeExamplesofFittingandCheckingTransferFunctionModels　435
11.4.1　FittingandCheckingoftheGasFurnaceModel　435
11.4.2　SimulatedExamplewithTwoInputs　441
11.5　ForecastingUsingLeadingIndicators　444
11.5.1　MinimumMeanSquareErrorForecast　444
11.5.2　ForecastofC02OutputfromGasFurnace　448
11.5.3　ForecastofNonstationarySalesDataUsingaLeadingIndicator　451
11.6　SomeAspectsoftheDesignofExperimentstoEstimateTransferFunctions　453
A11.1　UseofCrossSpectralAnalysisforTransferFunctionModelIdentification　455
All.I.1　IdentificationofSingleInputTransferFunctionModels　455
All.l.2　IdentificationofMultipleInputTransferFunctionModels　456
AI1.2　ChoiceofInputtoProvideOptimalParameterEstimates　457
All.2.1　DesignofOptimalInputsforaSimpleSystem　457
All.2.2　NumericalExample　460

12　INTERVENTIONANALYSISMODELSANDOUTLIERDETECTION　462
12.1　InterventionAnalysisMethods　462
12.1.1　ModelsforInterventionAnalysis　462
12.1.2　ExampleofInterventionAnalysis　465
12.1.3　NatureoftheMLEforaSimpleLevelChangeParameterModel　466
12.2　OutlierAnalysisforTimeSeries　469
12.2.1　ModelsforAdditiveandInnovationalOutliers　469
12.2.2　EstirmationofOutlierEffectforKnownTimingoftheOutlier　470
12.2.3　IterativeProcedureforOutlierDetection　471
12.2.4　ExamplesofAnalysisofOutliers　473
12.3　EstimationforARMAModelsWithMissingValues　474

PartIV　DesignofDiscreteControlSchemes　481

13　ASPECTSOFPROCESSCONTROL　483
13.1　ProcessMonitoringandProcessAdjustment　484
13.1.1　ProcessMonitoring　484
13.1.2　ProcessAdjustment　487
13.2　ProcessAdjustmentUsingFeedbackControl~488
13.2.1　FeedbackAdjustmentChart　489
13.2.2　ModelingtheFeedbackLoop　492
13.2.3　SimpleModelsforDisturbancesandDynamics　493
13.2.4　GeneralMinimumMeanSquareErrorFeedbackControlSchemes　497
13.2.5　ManualAdjustmentforDiscreteProportional-IntegralSchemes　499
13.2.6　ComplementaryRolesofMonitoringandAdjustment　503
13.3　ExcessiveAdjustmentSometimesRequiredbyMMSEControl　505
13.3.1　ConstrainedControl　506
13.4　MinimumCostControlWithFixedCostsofAdjustmentAndMonitoring　508
13.4.1　BoundedAdjustmentSchemeforFixedAdjustmentCost　508
13.4.2　IndirectApproachforObtainingaBoundedAdjustmentScheme　510
13.4.3　InclusionoftheCostofMonitoring　511
13.5　MonitoringValuesofParametersofForecastingandFeedbackAdjustmentSchemes　514
A13.1　FeedbackControlSchemesWheretheAdjustmentVarianceIsRestricted　516
A13.1.1　DerivationofOptimalAdjustment　517
A13.2　ChoiceoftheSamplingInterval　526
A13.2.1　IllustrationoftheEffectofReducingSamplingFrequency　526
A13.2.2　SamplinganIMA(O,I,I)Process　526

PartV　ChartsandTables　531

COLLECTIONOFTABLESANDCHARTS　533
COLLECTIONOFTIMESERIESUSEDFOREXAMPLESINTHETEXTANDINEXERCISES　540
REFERENCES　556

PartVI　EXERCISESANDPROBLEMS　569

INDEX　589
内容简介:
　　本书自1970年初版以来，不断修订再版，以其经典性和权威性成为有关时间序列分析领域书籍的典范。书中涉及时间序列随机(统计)模型的建立及许多重要的应用领域的使用，包括预测，模型的描述、估计、识别和诊断，动态关系的传递函数的识别、拟合及检验，干预事件影响的建模和过程控制等专题。本书叙述简明，强调实际技术，配有大量实例。
　　本书可作为统计和相关专业高年级本科生或研究生教材，也可以作为统计专业技术人员的参考书。
作者简介:
　　GeorgeE.P.Box国际级统计学家。曾于1960年创立威斯康星大学统计系并任该系主任，现为该校名誉教授。BOX发表过200多篇论文，出版过很多重要著作，其中本书和STATISTICEFOR
　　EXPERIMENTERS为其代表作。
　　GwilymM.Jenkins已故国际级统计学家。曾于1966年创立了英国兰开斯特大学系统工程系。JENKINS与BOX合作的成果对时间序列分析方法的研究和应用产生了巨大的推动作用。
　　GregoryC.Reinsel已故国际级统计学家。1995-1997年任威斯康星大学统计系系主任。因在统计领域的突出贡献而被推举为美国统计协会会士。
目录:
1　INTRODUCTION　1
1.1　FourImportantPracticalProblems　2
1.1.1　ForecastingTimeSeries　2
1.1.2　EstimationofTransferFunctions　3
1.1.3　AnalysisofEffectsofUnusualInterventionEventsToaSystem　4
1.1.4　DiscreteControlSystems　5
1.2　StochasticandDeterministicDynamicMathematicalModels　7
1.2.1　StationaryandNonstationaryStochasticModelsforForecastingandControl　7
1.2.2　TransferFunctionModels　12
1.2.3　ModelsforDiscreteControlSystems　14
1.3　BasicIdeasinModelBuilding　16
1.3.1　Parsimony　16
1.3.2　IterativeStagesintheSelectionofaModel　16

PartI　StochasticModelsandTheirForecasting　19

2　AUTOCORRELATIONFUNCTIONANDSPECTRUMOFSTATIONARYPROCESSES　21
2.1　AutocorrelationPropertiesofStationaryModels　21
2.1.1　TimeSeriesandStochasticProcesses　21
2.1.2　StationaryStochasticProcesses　23
2.1.3　PositiveDefinitenessandtheAutocovarianceMatrix　26
2.1.4　AutocovarianceandAutocorrelationFunctions　29
2.1.5　EstimationofAutocovarianceandAutocorrelationFunctions　30
2.1.6　StandardErrorofAutocorrelationEstimates　32
2.2　SpectralPropertiesofStationaryModels　35
2.2.1　PeriodogramofaTimeSeries　35
2.2.2　AnalysisofVariance　36
2.2.3　SpectrumandSpectralDensityFunction　37
2.2.4　SimpleExamplesofAutocorrelationandSpectralDensityFunctions　41
2.2.5　AdvantagesandDisadvantagesoftheAutocorrelationandSpectralDensityFunctions　43
A2.1　LinkBetweentheSampleSpectrumandAutocovarianceFunctionEstimate　44

3　LINEARSTATIONARYMODELS　46
3.1　GeneralLinearProcess　46
3.1.1　TwoEquivalentFormsfortheLinearProcess　46
3.1.2　AutocovarianceGeneratingFunctionofaLinearProcess　49
3.1.3　StationarityandInvertibilityConditionsforaLinearProcess　50
3.1.4　AutoregressiveandMovingAverageProcesses　52
3.2　AutoregressiveProcesses　54
3.2.1　StationarityConditionsforAutoregressiveProcesses　54
3.2.2　AutocorrelationFunctionandSpectrumofAutoregressiueProcesses　55
3.2.3　First-OrderAutoregressive(Markov)Process　58
3.2.4　Second-OrderAutoregressiveProcess　60
3.2.5　PartialAutocorrelationFunction　64
3.2.6　EstimationofthePartialAutocorrelationFunction　67
3.2.7　StandardErrorsofPartialAutocorrelationEstimates　68
3.3　MovingAverageProcesses　69
3.3.1　InvertibilityConditionsforMovingAverageProcesses　69
3.3.2　AutocorrelationFunctionandSpectrumofMovingAverageProcesses　70
3.3.3　First-OrderMovingAverageProcess　72
3.3.4　Second-OrderMovingAverageProcess　73
3.3.5　DualityBetweenAutoregressiveandMovingAverageProcesses　75
3.4　MixedAutoregressive-MovingAverageProcesses　77
3.4.1　StationarityandInvertibilityProperties　77
3.4.2　AutocorrelationFunctionandSpectrumofMixedProcesses　78
3.4.3　First-OrderAutoregressive-First-OrderMovingAverageProcess　80
3.4.4　Summary　83
A3.1　AutocovariancesAutocovarianceGeneratingFunctionandStationarityConditionsforaGeneralLinearProcess　85
A3.2　RecursiveMethodforCalculatingEstimatesofAutoregressiveParameters　87

4　LINEARNONSTATIONARYMODELS　89
4.1　AutoregressiveIntegratedMovingAverageProcesses　89
4.1.1　NonstationaryFirst-OrderAutoregressiveProcess　89
4.1.2　GeneralModelforaNonstationaryProcessExhibitingHomogeneity　92
4.1.3　GeneralFormoftheAutoregressiveIntegratedMovingAverageProcess　96
4.2　ThreeExplicitFormsfortheAutoregressiveIntegratedMovingAverageModel　99
4.2.1　DifferenceEquationFormoftheModel　99
4.2.2　RandomShockFormoftheModel　I00
4.2.3　InvertedFormoftheModel　106
4.3　IntegratedMovingAverageProcesses　109
4.3.1　IntegratedMovingAverageProcessofOrder(0,1,1)　110
4.3.2　IntegratedMovingAverageProcessofOrder(0,2,2)　114
4.3.3　GeneralIntegratedMovingAverageProcessofOrder(0,d,q)　118
A4.1　LinearDifferenceEquations　120
A4.2　IMA(0,1,1)ProcessWithDeterministicDrift　125
A4.3　ARIMAProcessesWithAddedNoise　126
A4.3.1　SumofTwoIndependentMovingAverageProcesses　126
A4.3.2　EffectofAddedNoiseontheGeneralModel　127
A4.3.3　ExampleforanIMA(O,1,1)ProcesswithAddedWhiteNoise　128
A4.3.4　RelationBetweentheIMA(O,1,1)ProcessandaRandomWalk　129
A4.3.5　AutocovarianceFunctionoftheGeneralModelwithAddedCorrelatedNoise　129

5　FORECASTING　131
5.1　MinimumMeanSquareErrorForecastsandTheirProperties　131
5.1.1　DerivationoftheMinimumMeanSquareErrorForecasts　133
5.1.2　ThreeBasicFormsfortheForecast　135
5.2　CalculatingandUpdatingForecasts　139
5.2.1　ConvenientFormatfortheForecasts　139
5.2.2　CalculationoftheψWeights　139
5.2.3　UseoftheψWeightsinUpdatingtheForecasts　141
5.2.4　CalculationoftheProbabilityLimitsoftheForecastsatAnyLeadTime　142
5.3　ForecastFunctionandForecastWeights　145
5.3.1　EventualForecastFunctionDeterminedbytheAutoregressiveOperator　146
5.3.2　RoleoftheMooingAverageOperatorinFixingtheInitialValues　147
5.3.3　LeadlForecastWeights　148
5.4　ExamplesofForecastFunctionsandTheirUpdating　151
5.4.1　ForecastinganIMA(O,1,1)Process　151
5.4.2　ForecastinganIMA(O,2,2)Process　154
5.4.3　ForecastingaGeneralIMA(O,d,q)Process　156
5.4.4　ForecastingAutoregressiveProcesses　157
5.4.5　Forecastinga(1,O,1)Process　160
5.4.6　Forecastinga(1,1,1)Process　162
5.5　UseofStateSpaceModelFormulationforExactForecasting　163
5.5.1　StateSpaceModelRepresentationfortheARIMAProcess　163
5.5.2　KalmanFilteringRelationsforUseinPrediction　164
5.6　Summary　166
A5.1　CorrelationsBetweenForecastErrors　169
A5.1.1　AutocorrelationFunctionofForecastErrorsatDifferentOrigins　169
A5.1.2　CorrelationBetweenForecastErrorsattheSameOriginwithDifferentLeadTimes　170
A5.2　ForecastWeightsforAnyLeadTime　172
A5.3　ForecastinginTermsoftheGeneralIntegratedForm　174
A5.3.1　GeneralMethodofObtainingtheIntegratedForm　174
A5.3.2　UpdatingtheGeneralIntegratedForm　176
A5.3.3　ComparisonwiththeDiscountedLeastSquaresMethod　176

PartII　StochasticModelBuilding　181

6　MODELDENTIFICATION　183
6.l　ObjectivesofIdentification　183
6.1.1　StagesintheIdentificationProcedure　184
6.2　IdentificationTechniques　184
6.2.1　UseoftheAutocorrelationandPartialAutocorrelationFunctionsinIdentification　184
6.2.2　StandardErrorsforEstimatedAutocorrelationsandPartialAutocorrelations　188
6.2.3　IdentificationofSomeActualTimeSeries　188
6.2.4　SomeAdditionalModelIdentificationTools　197
6.3　InitialEstimatesfortheParameters　202
6.3.1　UniquenessofEstimatesObtainedfromtheAutocovarianceFunction　202
6.3.2　InitialEstimatesforMovingAverageProcesses　202
6.3.3　InitialEstimatesforAutoregressiveProcesses　204
6.3.4　InitialEstimatesforMixedAutoregressive-MovingAverageProcesses　206
6.3.5　ChoiceBetweenStationaryandNonstationaryModelsinDoubtfulCases　207
6.3.6　MoreFormalTestsforUnitRootsinARIMAModels　208
6.3.7　InitialEstimateofResidualVariance　211
6.3.8　ApproximateStandardErrorfor　212
6.4　ModelMultiplicity　214
6.4.1　MultiplicityofAutoregressive-MovingAverageModels　214
6.4.2　MultipleMomentSolutionsforMovingAverageParameters　216
6.4.3　UseoftheBackwardProcesstoDetermineStartingValues　218
A6.1　ExpectedBehavioroftheEstimatedAutocorrelationFunctionforaNonstationaryProcess　218
A6.2　GeneralMethodforObtainingInitialEstimatesoftheParametersofaMixedAutoregressive-MovingAverageProcess　220

7　MODELESTIMATION　224
7.l　StudyoftheLikelihoodandSumofSquaresFunctions　224
7.1.1　LikelihoodFunction　224
7.1.2　ConditionalLikelihoodforanARIMAProcess　226
7.1.3　ChoiceofStartingValuesforConditionalCalculation　227
7.1.4　UnconditionalLikelihood;SumofSquaresFunction;LeastSquaresEstimates　228
7.1.5　GeneralProcedureforCalculatingtheUnconditionalSumofSquares　233
7.1.6　GraphicalStudyoftheSumofSquaresFunction　238
7.1.7　Descriptionof“Well-Behaved”EstimationSituations;ConfidenceRegions　241
7.2　NonlinearEstimation　248
7.2.1　GeneralMethodofApproach　248
7.2.2　NumericalEstimatesoftheDerivatives　249
7.2.3　DirectEvaluationoftheDerivatives　251
7.2.4　GeneralLeastSquaresAlgorithmfortheConditionalModel　252
7.2.5　SummaryofModelsFittedtoSeriesAtoF　255
7.2.6　Large-SampleInformationMatricesandCovarianceEstimates　256
7.3　SomeEstimationResultsforSpecificModels　259
7.3.1　AutoregressiveProcesses　260
7.3.2　MovingAverageProcesses　262
7.3.3　MixedProcesses　262
7.3.4　SeparationofLinearandNonlinearComponentsinEstimation　263
7.3.5　ParameterRedundancy　264
7.4　EstimationUsingBayesTheorem　267
7.4.1　BayesTheorem　267
7.4.2　BayesianEstimationofParameters　269
7.4.3　AutoregressiveProcesses　270
7.4.4　MovingAverageProcesses　272
7.4.5　Mixedprocesses　274
7.5　LikelihoodFunctionBasedonTheStateSpaceModel　275
A7.1　ReviewofNormalDistributionTheory　279
A7.1.1　PartitioningofaPositive-DefiniteQuadraticForm　279
A7.1.2　TwoUsefulIntegrals　280
A7.1.3　NormalDistribution　281
A7.1.4　Studentst-Distribution　283
A7.2　ReviewofLinearLeastSquaresTheory　286
A7.2.1　NormalEquations　286
A7.2.2　EstimationofResidualVariance　287
A7.2.3　CovarianceMatrixofEstimates　288
A7.2.4　ConfidenceRegions　288
A7.2.5　CorrelatedErrors　288
A7.3　ExactLikelihoodFunctionforMovingAverageandMixedProcesses　289
A7.4　ExactLikelihoodFunctionforanAutoregressiveProcess　296
A7.5　ExamplesoftheEffectofParameterEstimationErrorsonProbabilityLimitsforForecasts　304
A7.6　SpecialNoteonEstimationofMovingAverageParameters　307

8　MODELDIAGNOSTICCHECKING　308
8.1　CheckingtheStochasticModel　308
8.1.1　GeneralPhilosophy　308
8.1.2　Overfitting　309
8.2　DiagnosticChecksAppliedtoResiduals　312
8.2.1　AutocorrelationCheck　312
8.2.2　PortmanteauLack-of-FitTest　314
8.2.3　ModelInadequacyArisingfromChangesinParameterValues　317
8.2.4　ScoreTestsforModelChecking　318
8.2.5　CumulativePeriodogramCheck　321
8.3　UseofResidualstoModifytheModel　324
8.3.1　NatureoftheCorrelationsintheResidualsWhenanIncorrectModelIsUsed　324
8.3.2　UseofResidualstoModifytheModel　325

9　SEASONALMODELS　327
9.1　ParsimoniousModelsforSeasonalTimeSeries　327
9.1.1　FittingversusForecasting　328
9.1.2　SeasonalModelsInvolvingAdaptiveSinesandCosines　329
9.1.3　GeneralMultiplicativeSeasonalModel　330
9.2　RepresentationoftheAirlineDatabyaMultiplicative(0,1,1)~(0,1,1)12SeasonalModel　333
9.2.1　Multiplicative(0,l,l)~(0,l,1)12Model　333
9.2.2　Forecasting　334
9.2.3　Identification　341
9.2.4　Estimation　344
9.2.5　DiagnosticChecking　349
9.3　SomeAspectsofMoreGeneralSeasonalModels　351
9.3.1　MultiplicativeandNonmultiplicativeModels　351
9.3.2　Identification　353
9.3.3　Estimation　355
9.3.4　EventualForecastFunctionsforVariousSeasonalModels　355
9.3.5　ChoiceofTransformation　358
9.4　StructuralComponentModelsandDeterministicSeasonalComponents　359
9.4.1　DeterministicSeasonalandTrendComponentsandCommonFactors　360
9.4.2　ModelswithRegressionTermsandTimeSeriesErrorTerms　361
A9.1　AutocovariancesforSomeSeasonalModels　366

PartIII　TransferFunctionModelBuilding　371

10　TRANSFERFUNCTIONMODELS　373
10.1　LinearTransferFunctionModels　373
10.1.1　DiscreteTransferFunction　374
10.1.2　ContinuousDynamicModelsRepresentedbyDifferentialEquations　376
10.2　DiscreteDynamicModelsRepresentedbyDifferenceEquations　381
10.2.1　GeneralFormoftheDifferenceEquation　381
10.2.2　NatureoftheTransferFunction　383
10.2.3　First-andSecond-OrderDiscreteTransferFunctionModels　384
10.2.4　RecursiveComputationofOutputforAnyInput　390
10.2.5　TransferFunctionModelswithAddedNoise　392
10.3　RelationBetweenDiscreteandContinuousModels　392
10.3.1　ResponsetoaPulsedInput　393
10.3.2　RelationshipsforFirst-andSecond-OrderCoincidentSystems　395
10.3.3　ApproximatingGeneralContinuousModelsbyDiscreteModels　398
A10.1　ContinuousModelsWithPulsedInputs　399
A10.2　NonlinearTransferFunctionsandLinearization　404

11　IDENTIFICATIONFITTINGANDCHECKINGOFTRANSFERFUNCTIONMODELS　407
ll.1　CrossCorrelationFunction　408
11.1.1　PropertiesoftheCrossCovarianceandCrossCorrelationFunctions　408
11.1.2　EstimationoftheCrossCovarianceandCrossCorrelationFunctions　411
11.1.3　ApproximateStandardErrorsofCrossCorrelationEstimates　413
11.2　IdentificationofTransferFunctionModels　415
11.2.1　IdentificationofTransferFunctionModelsbyPrewhiteningtheInput　417
11.2.2　ExampleoftheIdentificationofaTransferFunctionModel　419
11.2.3　IdentificationoftheNoiseModel　422
11.2.4　SomeGeneralConsiderationsinIdentifyingTransferFunctionModels　424
11.3　FittingandCheckingTransferFunctionModels　426
11.3.1　ConditionalSumofSquaresFunction　426
11.3.2　NonlinearEstimation　429
11.3.3　UseofResidualsforDiagnosticChecking　431
11.3.4　SpecificChecksAppliedtotheResiduals　432
11.4　SomeExamplesofFittingandCheckingTransferFunctionModels　435
11.4.1　FittingandCheckingoftheGasFurnaceModel　435
11.4.2　SimulatedExamplewithTwoInputs　441
11.5　ForecastingUsingLeadingIndicators　444
11.5.1　MinimumMeanSquareErrorForecast　444
11.5.2　ForecastofC02OutputfromGasFurnace　448
11.5.3　ForecastofNonstationarySalesDataUsingaLeadingIndicator　451
11.6　SomeAspectsoftheDesignofExperimentstoEstimateTransferFunctions　453
A11.1　UseofCrossSpectralAnalysisforTransferFunctionModelIdentification　455
All.I.1　IdentificationofSingleInputTransferFunctionModels　455
All.l.2　IdentificationofMultipleInputTransferFunctionModels　456
AI1.2　ChoiceofInputtoProvideOptimalParameterEstimates　457
All.2.1　DesignofOptimalInputsforaSimpleSystem　457
All.2.2　NumericalExample　460

12　INTERVENTIONANALYSISMODELSANDOUTLIERDETECTION　462
12.1　InterventionAnalysisMethods　462
12.1.1　ModelsforInterventionAnalysis　462
12.1.2　ExampleofInterventionAnalysis　465
12.1.3　NatureoftheMLEforaSimpleLevelChangeParameterModel　466
12.2　OutlierAnalysisforTimeSeries　469
12.2.1　ModelsforAdditiveandInnovationalOutliers　469
12.2.2　EstirmationofOutlierEffectforKnownTimingoftheOutlier　470
12.2.3　IterativeProcedureforOutlierDetection　471
12.2.4　ExamplesofAnalysisofOutliers　473
12.3　EstimationforARMAModelsWithMissingValues　474

PartIV　DesignofDiscreteControlSchemes　481

13　ASPECTSOFPROCESSCONTROL　483
13.1　ProcessMonitoringandProcessAdjustment　484
13.1.1　ProcessMonitoring　484
13.1.2　ProcessAdjustment　487
13.2　ProcessAdjustmentUsingFeedbackControl~488
13.2.1　FeedbackAdjustmentChart　489
13.2.2　ModelingtheFeedbackLoop　492
13.2.3　SimpleModelsforDisturbancesandDynamics　493
13.2.4　GeneralMinimumMeanSquareErrorFeedbackControlSchemes　497
13.2.5　ManualAdjustmentforDiscreteProportional-IntegralSchemes　499
13.2.6　ComplementaryRolesofMonitoringandAdjustment　503
13.3　ExcessiveAdjustmentSometimesRequiredbyMMSEControl　505
13.3.1　ConstrainedControl　506
13.4　MinimumCostControlWithFixedCostsofAdjustmentAndMonitoring　508
13.4.1　BoundedAdjustmentSchemeforFixedAdjustmentCost　508
13.4.2　IndirectApproachforObtainingaBoundedAdjustmentScheme　510
13.4.3　InclusionoftheCostofMonitoring　511
13.5　MonitoringValuesofParametersofForecastingandFeedbackAdjustmentSchemes　514
A13.1　FeedbackControlSchemesWheretheAdjustmentVarianceIsRestricted　516
A13.1.1　DerivationofOptimalAdjustment　517
A13.2　ChoiceoftheSamplingInterval　526
A13.2.1　IllustrationoftheEffectofReducingSamplingFrequency　526
A13.2.2　SamplinganIMA(O,I,I)Process　526

PartV　ChartsandTables　531

COLLECTIONOFTABLESANDCHARTS　533
COLLECTIONOFTIMESERIESUSEDFOREXAMPLESINTHETEXTANDINEXERCISES　540
REFERENCES　556

PartVI　EXERCISESANDPROBLEMS　569

INDEX　589

查看详情

时间序列分析：预测与控制

内容简介:

作者简介:

目录: